Abstract
In this study we analyze symmetry group properties of the Benney system in the Eulerian description, which is in the form of the system of the coupled nonlinear integro-differential equations. We, first, find symmetry groups and obtain reduced forms, and then seek some similarity solutions to the reduced forms of the Benney equations. In addition, it is shown that one may transform solutions of the reduced forms of the Benney system into solutions of the reduced form of the one-dimensional shallow-water equations.
| Original language | English |
|---|---|
| Pages (from-to) | 241-254 |
| Number of pages | 14 |
| Journal | Mechanics Research Communications |
| Volume | 32 |
| Issue number | 3 |
| DOIs | |
| Publication status | Published - May 2005 |
Funding
This research is a part of author’s postdoctoral studies completed during his appointment at Massachusetts Institute of Technology, Department of Mechanical Engineering, USA, 2000–2003. It was partly supported by the NATO-TÜBİTAK (The Scientific and Technical Research Council of Turkey) fellowship. In addition, the author would like to thank the referees for their valuable comments that helped him to improve the paper.
| Funders | Funder number |
|---|---|
| NATO-TÜBİTAK | |
| Türkiye Bilimsel ve Teknolojik Araştirma Kurumu |
Keywords
- Benney equations
- Integro-differential equations
- Lie point symmetries
- Shallow-water equations
- Similarity solutions
- Symmetry groups